Professor Melander's current research focuses on fundamental issues in vortex dynamics and statistical fluid mechanics. His topics include vortex/boundary interactions in 2-D, morphology of vortex interactions in 2- and 3-D, identification of underlying mechanisms, topological description of 3-D viscous flows in terms of global bifurcation analysis of the vorticity field (i.e., vortex line history), construction and analysis of shell models of turbulence, statistical behavior of ensembles of shell model solutions, and the transition to turbulence in shell models.
Professor Melander's research is problem-driven and thus employs tools from classical and applied mathematics, numerical analysis, and scientific computation. Concepts from dynamical systems play a central role. His publications have appeared in the Journal of Fluid Mechanics, Physics of Fluids, Physical Review Letters, Fluid Dynamics Research, Physica D, and Physical Review E.